To estimate the slowness vector of infrasound waves propagating across an infrasound array, it is often considered that the sensors are located in a perfectly horizontal plane (2D approximation). However, the arrays are not planar and differences between sensor altitudes cannot be neglected without introducing biases when estimating the parameters of interest (back-azimuth and incidence).
A closed-formula of this error depending on the geometry of the array and the wave incidence is presented. Since the unbiased 3D estimation of the slowness parameters results in a significant alteration of the variance, a metric based on the mean square error is proposed. We found it useful to compare the 3D to the 2D processed results. We show the 3D estimator does not always give the best estimates. We propose also a formulation of the boundary that allow us to choose between these two estimators depending on the situation (arrays, incidence, and SNR). Finally we compare these two approaches (2D/3D) to all IMS arrays with synthetic data, and perform a comparative estimation of back-azimuth for real data.